On calculation of fractal dimension of images

Bisoi, Ajay Kumar; Mishra, Jibitesh

doi:10.1016/s0167-8655(00)00132-x

Cited by 123 publications

(59 citation statements)

References 11 publications

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“…Because the box-counting dimension is determined by the cover of an identical shape set, its calculation is easier than for other dimensions, and it is often used in geographical research. Therefore, we use the box-counting dimension ( Figure 5) to calculate the 3D fractal dimensions of LiDAR feature points [40]. To calculate the box-counting dimension, first, we use a cube to completely cover the entire feature point cloud without cracks and count the non-empty cube number N; the dimension is defined as…”

Section: Three-dimensional Fractal Dimensionmentioning

confidence: 99%

The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses

et al. 2015

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Light Detection and Ranging (LiDAR), a high-precision technique used for acquiring three-dimensional (3D) surface information, is widely used to study surface vegetation information. Moreover, the extraction of a vegetation point set from the LiDAR point cloud is a basic starting-point for vegetation information analysis, and an important part of its further processing. To extract the vegetation point set completely and to describe the different spatial morphological characteristics of various features in a LiDAR point cloud, we have used 3D fractal dimensions. We discovered that every feature has its own distinctive 3D fractal dimension interval. Based on the 3D fractal dimensions of tall trees, we propose a new method for the extraction of vegetation using airborne LiDAR. According to this method, target features can be distinguished based on their morphological characteristics. The non-ground points acquired by filtering are processed by region growing segmentation and the morphological characteristics are evaluated by 3D fractal dimensions to determine the features required for the determination of the point set for tall trees. Avon, New York, USA was selected as the study area to test the method and the result proves the method's efficiency. Thus, this approach is feasible. Additionally, the method uses the 3D OPEN ACCESSRemote Sens. 2015, 7 10816 coordinate properties of the LiDAR point cloud and does not require additional information, such as return intensity, giving it a larger scope of application.

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Section: Three-dimensional Fractal Dimensionmentioning

confidence: 99%

The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses

et al. 2015

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“…Fractal geometry also gives a mathematical special model of various difficult objects initiate in nature [1][2][3], that includes coastline, mountains, and clouds and also it has been useful in different texture analysis such as segmentation [4][5][6], shape measurement and classification [7], image and graphic analysis in different fields [8,9]. In this regard, different researchers are contributed their work, such as Gangepain and Roques-carmes presented reticular cell counting method [10,11] and later on Keller et al proposed probability box counting [10,12]. Both Gangepain and Keller gives the satisfactory result, but after reaching a particular level of image intensity surface then the slope of the arc tends to zero; therefore both the methods does not estimate the accurate FD.…”

Section: Introductionmentioning

confidence: 99%

“…al. presented a novel technique called differential box-counting (DBC) technique [4,10,13], this DBC method treated as the efficient one found in many articles like [14,15]. However in the case of DBC method there are three major problems reported by Jain et.…”

Section: Introductionmentioning

confidence: 99%

On Calculation of Fractal Dimension of Color Images

Nayak¹,

Mishra²

2017

IJIGSP

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Abstract-Fractal Dimension is a basic parameter of fractal geometry and it has been applied in many fields of application including image analysis, texture segmentation, and shape classification. Many fractal dimensions methods have been evolved depending upon different types of images that could be differentiated with greater precision. In this paper, we propose a color approach based on the modified differential box-counting method to estimate fractal dimension of color images in terms of its smoothness. Here we have experimented on four sets of color images like; sixteen number of real natural texture images, eight sets of controlled experimental fabric images with varied color and texture, twelve numbers of generated synthetic images and four smoothed images of known fractal dimension. The results demonstrated that the said proposed method shows accurate fractal dimension estimation of color texture image and also it indicates FD as 2 for smoothed images, which has already been developed in last decade and indicates higher roughness in color images, to check the accuracy of our proposed method, we used a set of twelve synthetic generated images.

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“…Fortunately, fractal theory is used to analyze the distribution of complex graphics. It has been widely used in art, astronomy, geography, biology, fluid dynamics, probability theory, chaos theory, and pure mathematics in the past few decades [14][15][16][17][18][19]. In recent years, the fractal theory was used to describe the propagation of cracks in rock or concrete specimens in laboratory [20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

A New Health Assessment Index of Tunnel Lining Based on the Digital Inspection of Surface Cracks

Wu¹,

Jiang²,

Wang³

et al. 2017

Preprint

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Abstract:The stability assessment of aged tunnel linings are mainly evaluated based on the visual inspection, and the Tunnel-lining Crack Index (TCI) is one of the most widely used tunnel lining health assessment indexes in Japan. However, the intersection and distribution of cracks, which could influence the stability of tunnel lining greatly, were not considered in TCI. A new method was proposed for the health assessment of tunnel lining, which evaluated the lining states according to the fractal dimension of cracks. Based on the machine vision-based method, the crack image could be extracted efficiently. The fractal dimension of lining cracks in one span could be obtained in a few minutes. A series of comparative tests and field tests were conducted to evaluate the validity of this new method. The comparative tests confirmed that fractal dimension was able to characterize the density, width, and distribution of cracks. The intersection of cracks, which would increase the risk of lining collapse, could also increase the fractal dimension. The fractal dimensions of tunnel lining cracks were obtained according to the digital inspection test of Hidake Tunnel in Japan for all the 65 spans. Moreover, the TCI was obtained through statistical methods. The correlation between fractal dimension and TCI of tunnel lining was studied. The significance of the new evaluation index is that it can identify the unusual spans of tunnel lining and provide a basis for further internal testing. As a complement to the conventional visual inspection method, the fractal dimension of the cracks is a promising health assessment index.

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On calculation of fractal dimension of images

Cited by 123 publications

References 11 publications

The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses

The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses

On Calculation of Fractal Dimension of Color Images

A New Health Assessment Index of Tunnel Lining Based on the Digital Inspection of Surface Cracks

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